Concept explainers
(a)
To find: The lowest height of a seat.
(a)
Answer to Problem 43E
21 feet below the center
Explanation of Solution
Given information: As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
Calculation:
If the center of the wheel is the zero point and the diameter is 42 then the radius is 21.
And at the bottom you are 21 feet below the center.
(b)
To find: The equation of the midline.
(b)
Answer to Problem 43E
Explanation of Solution
Given information: As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
Calculation:
The diameter is 42, so that means the radius is 21.
The maximum height minus the diameter will give you the height off the ground, which is 4.
The midline is going to be the Ferris wheel’s height from the going added to tis radius, the midline is 25 feet.
Thus,
(c)
To find: The period of the function.
(c)
Answer to Problem 43E
Period is 20 seconds
Explanation of Solution
Given information:As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
Calculation:
If the wheel rotates 3 times a minute then it rotates every 20 seconds.
So the period is 20 seconds.
(d)
To write: A sine equation to model the height of a seat that was at the equilibrium point heading upward when the ride began.
(d)
Answer to Problem 43E
Explanation of Solution
Given information: As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
Calculation:
Determine the amplitude
Since the seat is heading upward when the ride began, A must be positive, so
A = 21
Determine h and k
Conclude the sine equation
(e)
To find: When the seat will reach the highest point for the first time, according to the model.
(e)
Answer to Problem 43E
5 seconds
Explanation of Solution
Given information: Entertainment: As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
Calculation:
If the wheel rotates 3 times in a minute then it rotates every 20 seconds and if we start at the equilibrium point, it will reach the maximum height after a quarter of a revolution,
Thus, after 5 seconds
(f)
To find: The height of the seat after 10 seconds, according to the model.
(f)
Answer to Problem 43E
0 feet (25 feet above the ground)
Explanation of Solution
Given information: As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
Calculation:
If the wheel rotates 3 times in a minute then it rotates every 20 seconds so the period is 2 seconds.
So after 10 seconds it has done half a revolution which means it will be back at the same height that it started at.
Thus, 0 feet (25 feet above ground)
Chapter 6 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Precalculus (10th Edition)
University Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
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